一种离散强制型有限体积边界嵌入方法的研究

发布时间：2018-05-09 08:54

本文选题：边界嵌入方法 + 动边界流动　；参考：《南京航空航天大学》2016年博士论文

【摘要】：动边界流动问题,如鱼类游动、鸟类飞行、人体心脏血液流动和军用飞机的武器投放等,是流体力学研究中的热点和难点。边界嵌入(IB:Immersed Boundary)方法可以使用固定网格模拟这类问题,近些年来受到了广泛的关注。本文对一种离散强制型有限体积IB方法展开研究,该方法本质上是一种通过边界附近解的近似形式,使得边界附近节点上控制方程的有限体积离散形式封闭的数值方法。根据"边界条件强制点"所处位置的不同,该方法又进一步分为当地DFD方法和有限体积HCIB方法。对当地DFD方法来说,"边界条件强制点"是解域外紧靠固壁边界的网格节点,对有限体积HCIB方法来说则是解域内紧靠固壁的节点。论文的主要研究工作有如下几个方面:(1)提出了不可压粘性流动模拟的有限体积HCIB方法。空间离散采用Garlerkin有限体积近似,采用结合了无滑移条件和简化动量方程的沿物面法向的二次多项式近似,确定边界嵌入点上的压强和速度,并将该方法推广到三维复杂几何外形动边界绕流问题的求解。与原始的有限差分HCIB相比,该方法不限于Cartesian网格,也适用于非结构网格;如果流场中同时存在静止和运动边界,仍然可以对静止边界采用传统的边界协调网格。与当地DFD方法相比,在处理薄物体绕流问题时不会出现多值点的情况,方法的实现要简单得多。(2)提出了无粘可压流动模拟的有限体积HCIB方法。空间离散同样采用Garlerkin有限体积近似。边界嵌入点上的法向速度由结合了壁面无穿透条件的线性内插决定,压强由简化的动量方程确定,密度和切向速度则由等熵和等总焓关系分别确定。通过引入当地本征坐标系,使这一方法推广至三维变得非常简单。与Cartesian Cut-cell方法相比,该方法不需要对单元作当地切割处理。与Ghost-cell和当地DFD方法相比,该方法可以避免繁琐的多值点处理过程以及因外插导致的误差增大。(3)针对当地DFD方法,提出了混合重构和附加质量源/汇两种改进措施。混合重构中,在最靠近物面边界的流体点上,通过当地DFD解和沿物面法向二次多项式近似解的加权平均进行解的重构,以实现该点上数值描述的平滑过渡。通过在连续方程中引入质量源汇项,提高当地DFD方法动边界流动模拟时的质量守恒性,质量源汇项的构建通过计算被浸没边界分割的控制体固体部分上的通量得到。这两种措施均能够在不影响原始DFD方法空间精度和几乎不增加计算量的前提下,有效地降低动边界流动模拟结果中的数值振荡。(4)针对流固耦合问题,发展了一种适用于模拟刚性和柔性物体的分区紧耦合方法,分析了紧耦合迭代的稳定性和收敛性,并针对附加质量效应显著的问题,提出了一种新型的适用于分区紧耦合策略的预估-校正方法以提高FSI的迭代效率。预估-校正方法中通过预估流固交界面处流体运动和固体运动的各种信息,减少校正过程所需的迭代步数,达到提高紧耦合效率的目的。预估-校正方法的意义在于:其基本思想可以应用到其他的SC-FSI求解器中,以提高耦合效率。采用本文的离散强制型有限体积IB方法求解流体方程,验证了其求解复杂流固耦合问题的可靠性。针对二维/三维、静止/运动、刚性/柔性物体的绕流,本文开展了大量的数值实验,并将计算结果与参考文献的数值结果或实验数据进行了比较,验证了所提出和发展的各种数值方法的准确性和可靠性。
[Abstract]:The dynamic boundary flow problem, such as fishes swimming, bird flight, human heart blood flow and military aircraft weapon delivery, is a hot and difficult point in the study of fluid mechanics. The boundary embedding (IB:Immersed Boundary) method can use fixed grid to simulate such problems. In recent years, it has received extensive attention. This paper is a kind of discrete coercion. The finite volume IB method is studied. This method is essentially a numerical method of finite volume discretization of the control equations on the nodes near the boundary by the approximate form near the boundary, which is further divided into the local DFD method and the finite volume HCI according to the different position of the "boundary condition coercion". B method. For local DFD method, "boundary condition coercion point" is a grid node that is close to the solid wall boundary outside the solution. For the finite volume HCIB method, it is a node close to the solid wall in the solution. The main research work of this paper is as follows: (1) a finite volume HCIB method for the incompressible viscous flow simulation is proposed. By using the finite volume approximation of Garlerkin, the two polynomial approximation, which combines the non slip condition and the simplified momentum equation, is used to determine the pressure and velocity on the boundary embedded point, and the method is extended to the solution of the flow problem in the three-dimensional complex geometric contour. Compared with the original finite difference HCIB, the method is not limited. The Cartesian grid is also suitable for unstructured grids. If there is a static and moving boundary in the flow field, the traditional boundary coordination grid can still be used on the stationary boundary. Compared with the local DFD method, the implementation of the method is much simpler in dealing with the problem of flow around a thin object. (2) a non sticky method is proposed. The finite volume HCIB method for the pressure flow simulation. The spatial discretization is also used for the Garlerkin finite volume approximation. The normal velocity on the boundary embedded point is determined by the linear interpolation combined with the wall without penetration condition. The pressure is determined by the simplified momentum equation, and the density and tangent velocity are determined by the isentropic and equal total enthalpy relations. The local eigencoordinate system is very simple to extend this method to 3D. Compared with the Cartesian Cut-cell method, this method does not require local cutting processing. Compared with the Ghost-cell and local DFD methods, this method can avoid cumbersome multivalue processing and increase the error caused by extrapolation. (3) local DFD side Two improvement measures are proposed in the method of mixed reconstruction and additional mass source / sink. In the mixed reconstruction, the solution is reconstructed by the local DFD solution and the weighted average of the approximate two polynomial approximate solution at the fluid point near the boundary of the surface, so as to realize the smooth transition of the numerical description on this point. Source and sink terms, improve the mass conservation of the dynamic boundary flow simulation in the local DFD method. The construction of the quality source and sink is obtained by calculating the flux on the solid part of the controlled body divided by the immersed boundary. These two measures can effectively reduce the moving edge without affecting the spatial accuracy of the original DFD method and almost without increasing the amount of calculation. The numerical oscillation in the boundary flow simulation results. (4) for the fluid solid coupling problem, a zonal tight coupling method suitable for the rigid and flexible objects is developed, and the stability and convergence of the tightly coupled iteration are analyzed. A new method is proposed for the subarea tight coupling strategy for the problem of the significant additional mass effect. The correction method is used to improve the iterative efficiency of FSI. The prediction correction method can reduce the number of iterative steps required for the correction process by predicting the various information of fluid motion and solid motion at the fluid solid interface. The significance of the predictor correction method is that its basic idea can be applied to other SC-FSI solutions. In order to improve the coupling efficiency, the discrete forced finite volume IB method in this paper is used to solve the fluid equation, and the reliability of the solution to the complex fluid solid coupling problem is verified. A large number of numerical experiments are carried out in this paper for two-dimensional / three-dimensional, static / motion, rigid / flexible body around the flow, and the calculation results are compared with the reference values. Compared with experimental data, the accuracy and reliability of various numerical methods proposed and developed are verified.

【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O241.82;O35

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